Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay

In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Caratheodory approximation approach and stochastic calculus to present the existence and uniqueness theorem of the stochastic system under Caratheodory-type conditions with Lipschitz and non-Lipschitz conditions as special cases. Some existing results are generalized and enhanced. Finally, an application is offered to illustrate the obtained theoretical results.

Automated summary

This manuscript studies a new class of impulsive fractional Caputo neutral stochastic differential equations perturbed by fractional Brownian motion and Poisson jumps. The existence and uniqueness theorem of the stochastic system under Caratheodory-type conditions with Lipschitz and non-Lipschitz conditions is presented using Caratheodory approximation approach and stochastic calculus, with some existing results being generalized and enhanced. Finally, an application is offered to illustrate the obtained theoretical results.